Open AccessDIRICHLET PROBLEM FOR PULKIN’S EQUATION IN A RECTANGULAR DOMAIN
Author(s) -
Rimma Safina
Publication year - 2014
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2014-20-10-91-101
Subject(s) - mathematics , uniqueness , mathematical analysis , bessel function , dirichlet problem , completeness (order theory) , boundary value problem , fourier series , convergence (economics) , series (stratigraphy) , paleontology , economics , biology , economic growth
In the given article for the mixed-type equation with a singular coecient the rst boundary value problem is studied. On the basis of property of completeness of the system of own functions of one-dimensional spectral problem the criterion of uniqueness is established. The solution the problem is constructed as the sum of series of Fourier - Bessel. At justication of convergence of a row there is a problem of small denominators. In connection with that the assessment about apartness of small denominator from zero with the corresponding asymptotic which allows to prove the convergence of the series constructed in a class of regular solutions under some restrictions is given.